Multi-dimensionally aware entropy stable and positivity preserving Godunov-type schemes for hydrodynamics on unstructured grid

：Raphaël Loubère（法国 University of Bordeaux）
：2023-12-15 10:20
：海韵园实验楼105报告厅

报告人：Raphaël Loubère（法国 University of Bordeaux）

时  间：2023年12月15日10:20

地  点：海韵园实验楼106报告厅

内容摘要:

In this talk, we propose to reuse the notion of simple Riemann solver in Lagrangian coordinates to develop a new Eulerian Finite Volume (FV) scheme in the multi-dimensional case on unstructured meshes. As a proof of concept, we entirely derive the associated first-order accurate cell-centered Eulerian scheme for compressible flows using the Lagrangian to Eulerian correspondence. First, the Lagrangian simple Riemann solver is used as a building block to construct its Eulerian counterpart. This solver inherits by construction the properties of the Lagrangian one, mainly: positivity preservation, entropy dissipation, well-defined CFL condition and wave-speed ordering. From this Riemann solver, a classical two-point first-order Finite Volume Eulerian scheme can be deduced for which the numerical fluxes of a given cell are computed only with respect to two neighbors through a common face. Next, we introduce another Eulerian numerical scheme which involves a multi-dimensional Lagrangian nodal solver, leading to the so-called multi-point Riemann solver that involves all surrounding cells, including corner cells. The conservation is no more relying on a one-to-one flux cancellation across a face like most FV approaches. Conversely, in this work, conservation is retrieved on a node basis. An associated first-order Eulerian scheme is derived on the basis of this multi-point nodal-based Riemann solver. We prove that this FV multi-point scheme still inherits some good properties with the extra-property of coupling all neighbor cells in a consistent way. A set of numerical results on general 2D unstructured grids are presented on several classical two-dimensional test cases, showing that the two-point scheme generates spurious instabilities such as the infamous carbuncle phenomena, while the multi-point scheme seems insusceptible to those.

个人简介：

Raphaël Loubère, Director of Research at CNRS, Institut de Mathématiques de Bordeaux (IMB), University of Bordeaux, France. He got his PhD in applied mathematics in 2002 from the University of Bordeaux, and then held a postdoc position for 3 years at the Los Alamos National Laboratory, U.S.A. In 2006 he won a CR CNRS position at the Mathematical Institute in Toulouse (IMT UMR 5219), and in 2016 he became a DR CNRS at IMB. His research mainly focuses on developing numerical methods that are used as simulation code engines. Those codes are dedicated to simulate complex physical phenomena, such as compressible fluids, multi-phase and multi-material flows, elasto-plastic material, magneto-hydrodynamics, inertial confinement fusion, etc. These fields of research were in close relationship with industrial partners who are the end-users of such innovative numerical methods run on massively parallel machines. He has published more than 70 articles in top-ranked international journals, including JCP, SINUM, SISC, etc.

 

联系人：邱建贤